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Register a new userInterlayer coherence and entanglement in bilayer quantum Hall states at filling factor $ u=2/lambda$
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We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $lambda$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlayer entanglement more effective and robust under perturbations than in the spin-frozen situation, mainly for a large number of flux quanta $lambda$. Interlayer entanglement of an equilibrium thermal state and its dependence with temperature and bias voltage is also studied for a pseudo-Zeeman interaction.
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We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ u=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ u =1$ and discovered at $ u =2$. In particular, three different $ u =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $ u=2/lambda$ ($lambda$ odd) and we also study the large $SU(4)$ isospin-$lambda$ limit. The model Hamiltonian is an adaptation of the $ u=2$ case [Z.F. Ezawa {it et al.}, Phys. Rev. {B71} (2005) 125318] to the many-body situation (arbitrary $lambda$ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeeman, tunneling, etc, control parameters) is obtained by using previously introduced Grassmannian $mathbb{G}^4_{2}=U(4)/[U(2)times U(2)]$ coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any $lambda$, but the phase transition points depend on $lambda$, and the instance $lambda=1$ is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly $lambda$ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.
We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $ u=2/lambda$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $lambda$. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space $mathbb{G}^4_{2}=U(4)/[U(2)times U(2)]$ (a higher-dimensional generalization of the Haldanes 2-dimensional sphere $mathbb{S}^2=U(2)/[U(1)times U(1)]$). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e., as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrodinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.
We develop a group-theoretical approach to describe $N$-component composite bosons as planar electrons attached to an odd number $f$ of Chern-Simons flux quanta. This picture arises when writing the Coulomb exchange interaction as a quantum Hall ferromagnet in terms of collective $U(N)$-spin operators. A spontaneously chosen ground state of $M$ electrons per Landau site breaks the symmetry from $U(N)$ to the stability subgroup $U(M)times U(N-M)$, so that coherent state excitations are labeled by points on the Grassmannian coset $U(N)/U(M)times U(N-M)$. The quantization of this Grassmann phase space corresponds to the carrier Hilbert space of unitary irreducible representations of $U(N)$ described by rectangular Young tableaux of $M$ rows and $f$ columns. We construct an embedding of the Hilbert space into Fock space by using a Schwinger realization of collective $U(N)$-spin operators as bilinear products of composite boson operators. We also build a system of Grassmann coherent states and discuss the classical limit of $U(N)$ quantum Hall ferromagnets in terms of nonlinear sigma models on Grasmannians.
Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor $ u=1$ and at very low temperatures($sim40$ mK). A small change in filling factor ($delta uapproxpm0.01$) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at $ u=1$ is surprisingly fragile against increasing temperature, or against small changes in filling factor.
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